Two wires $A$ and $B $ of same length and of the same material have the respective radii ${r_1}$ and ${r_2}$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of $A$ and the angle of twist at the end of $B $ will be
AIIMS 1980, Diffcult
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(c)Twisting couple $C = \frac{{\pi \eta {r^4}\theta }}{{2l}}$
If material and length of the wires $A$ and $B$ are equal and equal twisting couple are applied then
$\theta \propto \frac{1}{{{r^4}}}$ $\Rightarrow $ $\frac{{{\theta _1}}}{{{\theta _2}}} = {\left( {\frac{{{r_2}}}{{{r_1}}}} \right)^4}$
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